This document is a syntax summary of the MATHS notation.
The MATHS notation is designed so that mathemtical formulae and
definitions can be expressed in a palatable form by software developers
in ASCII.

It contains more than the norml Bachus-Normal-Form grammar because
a lot of special names need to be given meaning as well as syntax.

This document is a collection of formal (mathematical BNF-style)
definitions and assertions.
There are less formal introductions that may be easier to understand:
[ intro_characters.html ]
and
[ intro_ebnf.html ]
elsewhere.

MATHS has a number of predefined forms that are used to construct and define
new kinds of expressions: infix, prefix, unary, infix, functional, ... .
In the following (1st) stands for an expression and (2nd) for a
set of operators or functions. Each definition defines a set
of syntax forms like this PREFIX("-",numbers)="-" P(numbers).

Special characters are defined in
[ intro_characters.html ]
that also outlines the syntax of expressions and a document.

Proofs follow a natural deduction style that start with
assumptions ("Let") and continue to a consequence ("Close Let")
and then discard the assumptions and deduce a conclusion. Look
here
[ Block Structure in logic_25_Proofs ]
for more on the structure and rules.

The notation also allows you to create a new network of variables
and constraints. A "Net" has a number of variables (including none) and
a number of properties (including none) that connect variables.
You can give them a name and then reuse them. The schema, formal system,
or an elementary piece of documentation starts with "Net" and finishes "End of Net".
For more, see
[ notn_13_Docn_Syntax.html ]
for these ways of defining and reusing pieces of logic and algebra
in your documents. A quick example: a circle
might be described by
Net{radius:Positive Real, center:Point, area:=π*radius^2, ...}.

For a complete listing of pages in this part of my site by topic see
[ home.html ]

The notation used here is a formal language with syntax
and a semantics described using traditional formal logic
[ logic_0_Intro.html ]
plus sets, functions, relations, and other mathematical extensions.